Apparatus for combining variable quantities



Sept. 13, 1949. w. F. DEHN APPARATUS FOR COMBINING VARIABLE QUANTITIES Filed Sept. 15, 1945 4 Sheets-Sheet 1 32 FIG. i

/N VE N TOR w DEHN A TU OR/LE Y Sept 13, 1949. v w. F. DEHN 2,431,643

APPARATUS FOR COMBINING VARIABLE QUANTITIES Filed Sept. 15, 1943 4 Sheets-Sheet 2 FIG. 8

w FIG. 6

27 /36' I37 I38 /4/ I39 Imam ATTORNEY 35 20 A an 336 236 mt 335 I 235 I42 I lNVE/VTOR WE DEH/V R MM Sept. 13, 1949 w. F. DEHN APPARATUS FOR COMBINING VARIABLE QUANTITIES Filed Sept. 15, 1945 4 Sheets-Sheet 3 w. N N m m WM E A MD m F R V B m? Sept. 13, 1949. w. F. DEHN APPARATUS FOR COMBINING VARIABLE QUANTITIES Filed Sept. 15, 1943 v 4 Sheets-Sheet 4 efimwsum Patented Sept. 13, 1949 APPARATUS Foe o omei me vermin; QUANTITIES William F. Dchn, Nutley, N. J.,..asS.ig nr .tb

ern Electric Company,-lncorpprated, New York, N. Y., a corporation of New York Application September 15, 1943*, serial No. 502,546

This invention relates to apparatus for combini'ng variable quantities and more particularly to apparatus for indicating or recording or both indi'cating and recording the combined value of two or more continuously varying quantities or functions of such quantities'the combination being by .additiomsubtraction, multiplication or division. i r r Threa-re innumerable instances in many arts Where it is desired .to indicate, e. g. by a pointer moving over a scale, or to record, e. g. by a tracing point moving transversely to and fro on a longitudinally moving tape, the sum, difference, product o quotientof two or more varying quantities. For example, the total effective heat input to a closed oven chamber may be controlled by the indicated orrecorded sum of temperatures taken simultaneously atv a plurality of points with in the chamber,., Again, electric power is indi cated by the product of voltage and amperage of a current. v I I An object of the present invention is to provide apparatus to ,acceptftwo or more straight line motions representing respectively twoormore continu'ouslyjvar'ying' quantities; to combine these motions into a single" motion representing the sum, difierence, product or quotient of" the quantities,and to indicate" the instantaneous comb ined uantity, or to record continuously the comtabularly or graphically, and can be graphically e ie en edl V r, With the above and other objects in view a simpler form of the invention maybe embodied man appa tus comprisin a cam member drivable to a displacement proportional toone variable to be combined, a movable abutment to be displaced correspondingl-yl' -by the cam member, a second cam member shiftabl'e with the abutment and drivable transversely to the motion thereof to a displacement proportional to a second variable to be combined, a second movable abutment to be" displaced correspondingly by the second cam, and means'actuable by thesecond abutment to indicate" the motion thereof on a scale or to record ,thesaine on a moving recordsurface.

,0 e r objects and features of the. invention will:

are fr th .ivi q ma a d e e i n-oi embodimentsthereoitaken in connection with;-

the" accompanying drawings in whichv the same reference numerals are, applied to identical parts in the several figures and in which Fig. 1 is adiagrammatic view of one form-of embodiment to illustrate the principle of the in:-

vention; Fig. 2 is a similar view of a modified form; Fig. 3. is a similar view of another modification; Fig. 4 is a similar view of a third modification; Fig. 5is a similar view of a iourth modification; Fig. 6 is a similar view of. a fifthmodification; Fig. '7 is a view in'front elevation partly in section and with parts brcke'naway of a complete embodiment of the invention; g Fig. 8 is a horizontal section on the line 88 of Fig. 7; V

Fig. 9 is a vertical section on the line 9--9 of Fig. 7; .Fig. 10., is a detail section on the line Ill-I0 of Fig. 7, and

Fig. 11 a view similar to Fig. 7 of a modified form...

The firsts x fi ur s oft drawings ar presentedto, enable aneasy visualization of the range of applications of the invention. Thus, in Fig. 1 there is a fixed abutment 20.11pm which is support ed, 'a vertically freely shiftable and horizontallyddrivable cam wedge 2 l, Upon this cam rests a movable abutment slide 22 confined to free vercalm ionimly. ea by p n 23 d g in a uide slot the slide 22 rests a second vertical ly freely movable and horizontally drivable wedge cam; 25; and upon the cam .25 rests a second vertically movable slide 2lguided by pins 26 in the slot 24. A cord 28 fastened to the slide 2] runs over asheave29 to a weight 3%. A pointer Si is moved by the sheave over a scale 32. V

.Assume now that the wedge 21 is driven to the left and retracted to the right accordingas some varying value at increases and decreases; The slide 22 .will then be raised and lowered in strict proportion to the changing valu of a: and will carrythe wedge 25 and the slide 2! vertical-, 15/ up and down with itself. Let the wedge cam 251cc driven to the right and retracted to the left in accordance with the varying value of some otherv variable y in. similar fashion. Then the wedge 25 nasend lowers the slide 2? from'and toward the slide 22 in strict proportion to' the changing value of y. Since the slide 22 is already following the-varying value of as, the motion of the slide 2! will follow the changing value of the sum of a; and y, The distance from the top of the abutment 20 tothe bottom of the slide 21 is al: ways.aac+by+s, where s is the length of the slide 22, ,a is a constantratio proportional to 2 tan A (A being the apex angle of the wedge 2 I) by which the horizontal motion a: of the wedge 2I is converted into vertical motion of the slide 22, and b is a similar ratio for 3;. By suitable choice of A and B (making A equal to B in the simplest case where a: and y represent quantities of like kind, measured in the same units) and by suitably calibrating the scale 32, the pointer 3| will indicate the instantaneous algebraic sum of .r and y at all times and will follow the variations of (:z:+y) regardless of how a: and y individually vary. By substituting for the cord, pointer and scale of Fig. 1, a rod I28 carrying a marking point I3I which runs to and fro with the motion of the slide 21 transversely across a paper tape I32 or other suitable surface traveling with constant motion transverse to the motion of the point I3I, as illustrated in Fig. 2, there will be traced on the tape I32 a rectangular coordinate graph of the sum (a:+y) of the quantities in and y plotted against rtime. Although the wedge cams 2I and are shown as oppositely directed in Fig. 1, this is not a necessary relation. They may equally well be like directed, as are the wedge cams I2I and I25 of Fig. 2.

If the operating cams be formed, as in Fig. 2, with their cam surfaces shaped to follow the rectangular coordinate curve of the logarithmic function, then the pointer 3I will indicate on a suitably calibrated scale 32 the instantaneous value of the product of :r and 1 since the motion of the slide 2? will follow the sum of log at and log y, i. e. log my; or the point I3I will trace the graph of log my. Similarly, if the wedge cam 22I be shaped to the curve of the logarithm while the cam 225 is shaped to the curve of log l/y, as in Fig. 3, the indication or curve, as the case may be, will be of the value of the logarithm of the quotient :r/y.

In each of Figs. 1, 2 and 3, the operating cam 2|, 25, I2 I, I25 and 225 are shown as rectilinearly reciprocable wedges. They may, however, equally well be rotary cams 32I and 325 as in Fig. 4, which is equivalent to Fig. 1 in operation. In each of Figs. 1 and 2, the cams are shown as symmetrical about a horizontal axis. This is preferable in some instances; but in others it may be preferred to have a cam face on one side only as in Fig. 3. In each of Figs. 1, 2, 3 and 4 there are two operative cams and the indication or record is of the value of the sum, difierence, product or quotient of two varying quantities a: and 11. There may, however, within limits, be any number of operative cams. Fig. 5 shows an arrangement similar to Fig. 1, but having an additional slide 33 and cam 34 interposed between the cam 25 and slide 21, the aparatus then indicating the algebraic sum of :c, y and 2.

Fig. 6 illustrates the principles of a considerably developed form of the invention. Here the simple wedge 2I of Fig. l is replaced by a device generally indicated at 42I having a horizontally reciprocable cam base 35 on which is pivoted a cam member 36 so that the two together constitute a wedge cam on which the slide 22 rests. Slidably adjustable along the base 35 is a block 37 to alter the angle of the cam proper 35, and adjustable by means of a screw 38 running through a nut on the base 35. The wedge cam 25 of Fig. l is replaced by a similar assembly generally indicated at 425 and having corresponding elements I35, I36, I31, I38 and I39 respectively. The outer ends of the base members and I35 abut respectively against and are reciprocated by vertically reciprocable cam members 40 and I40 respectively and compression springs ll and I4I. The cams 40 and I40 are driven in turn by adjustable cam wedges 42 and I42 similar in structure to the devices 42I and 425.

Let the cam bases 235 and 335 be driven leftwardly and rightwardly respectively at the same constant speed t. The cams 40 and I40 are then driven upwardly at rates at and bt respectively, where a and b are constant coefficients dependent respectively upon tan A and tan B where A and B are the angles of slope of the members 236 and 336 with respect to the bases 235 and 335 respectively. The movement of 40 then is at and that of I 43 is bt. Let the cam faces of the cams 40 and I43 be shaped to flu) and F(u) respectively where f and F are any two desired functions of a I real variable which are single valued and continuous within the range of values of interest. The displacements of HI and 425 by the cams 40 and I40 then become flat) and F(bt) respectively. Taking the angles of slope of the cam bars 36 and I36 with respect to their bases as D and E respectively, the cam 42I drives the slide 22 up at a rate dflat) and the cam 425 drives the slide 21 at a rate eF(bt), where d and e are constants dependent upon tan D and tan E respectively. Thus, finally, the motion of the tracer point I3I is df(at) plus eFQJt), and if the tape I32 moves at appropriate constant speed to the left, the point I3I will trace thereonthe curve of the equation y=df(aa:) +eF(bx) where a and b may be adjusted to desired predetermined values by manipulation of the screws 238. and 338, d and e may be similarly set by the screws 33 and I38 respectively, and the functions ,f and F may be any desired, provided cams 40 and I40 can be cut to their curves. As before, although only two cams 42I and 425 in the vertical series are shown, the apparatus is not necessarily so limited, but may be extended to deal with any number of terms within reasonable limits. Thus the apparatus may be expanded to give instantaneous values or to construct the graph for a very wide range of expressions of the general type Thus if the cams 40, I40, etc. be cut to identical sine curves, all alike, by suitable adjustment of the cam bars, the apparatus may be set to sum a Fourier series to as many terms as there are cams 40, I40, etc. If the two cams of Fig. 6 are cut to the curves of the Bessel functions e. g.- those of zero order, Jo(;r) and Yo(:r;), the apparatus may be used to express mechanically the solution of the differential equation d y 1 dy whose general solution is 3/=C'1Jo(k:l:) +C2Yo(km) Figs. 1 to 6 inclusive and the above discussion of them are believed to explain clearly the general principles and something of the scope and general purport of the invention. Figs. 7 to 11 inclusive show two mechanically developed and operative embodiments in full detail. In Fig. 7 a pair of carriages 44 and 45, one above the other, run independently of each other and freely between vertical guide rails 46 and 4'! at the left of the apparatus-. Attheri'ght;similar carriages and 45 mm shn-ilarl y between vertical guide rails 5i] and= 5- l Between' the two sets of guide ra'i-l's' is 'a pain of ve'rtical standards '52 and 53,- one behind thecther; and-formed with vertical parallel guide slots 5' l and 55. In the-bettomof these slots rests a -shlait- 55 lraving a painof rollers 51} 5'lspaced watt and?ournalled thereonorrantif 'ction bear in'gss- Qntherouers '51,: e i rests a cam wedge 58 having itscenter cut out as shown at 59' in Figs". 7 and lili The left endf *this cam has a guide and supportrod 60' integral therewith or "rigidly secured thereto;extendinghorizontally into and slidable in' a' corresponding-bore in the carriage 45?" At the rigl'it'endl ofthecam 58 is: a similar rea 61: which is also' the i piston rod of a piston fiz 'in'a cylinder "fid'secured to the carriage 48;

OHi'thGWEd'gEEW rests. a pair of rollers 64,. 64; spaced apart and journal-led on ball hearings on a'shal t fi5 whose ends vertieally freelyislidable in th'ej slots 'd li and 55. Between the rollers 84, 64 isjournalled' similarly: a third roller 56; and on theirollsrfifi?rests the upper wedge cam 67 having omits left ezrdia piston rod 68"s'ecured to a "piston 692m a cylinder "10 on the carriage M. The wedge cant. 6]. also hason' its right end a guide rod H runningz'iri atcorresponding bore in the carriage 4:92 Onxthe wed'ge'filrests a roller l2 journalled on ballz bearings on a shaft 13 also vertically'freely slidable in the slots 5 l-and 55. 41 and 5| are slotted vertically at it and l5respectiVeIyKFigpQ) to=al-lowtherodsfiil and 68, and H and"! l ,=.to2movefreely :up and down. i

Afsti'rrupllfi mountedon the'shait 13 has a cord TI SECUI Bd'thGIG EOf running up-and over a sheave IBJandfdOvinto aweight 19;- On the pivot shaft of the sh'eave 1B is secured a pointer 'Strunning over a scale= 8 l-:

1 Theacylinder 634m the-carriage has its left end -wall' perforated with one or more apertures 82 to -allowair to enter-or escape 'freely therethroughi- The right end wall is solidly closed exceptifor a threaded bore to receive a nipple 83 secured liquid tight therein. At some point conveniently near a stationary support I48 carries ar cylinder'lifi3 havingz a'pis'ton I62, a -piston rod I611; air, apertures [32 and a nipple I83; 7 The nipple 83 is connected" to the nipple I83 by a fiexibleyinelastic; inextensiblehose 34; Similarly a-cylind'erfill mounted-on a convenientlylocated stationarysupport Midis-connected by'a hose: 85 to the cylinder Hi and has a piston rod H38;-

Assumdnojwthat the bores of the. cylinders Bland 53,3113 the sameand that the system from thedeft-side-of the piston I62 to theright side-of the piston 62 is filled completely with a suitable pressure transmittingliquid, e. g. water or oil. Assume/the same for the cylinders l0 and lit. Then anydisplacement a: of'the piston rod [61 will efiect a displacement of the piston rod 61 and hence of the cam 58 identical in direction and magnitude, thelpiston 62 beingdr-iven to the left by hydraulic pressure from the cylinder I63 and to the right by atmospheric pressure through the aperture 82. If the cam 58 be thus displaced to the left, it will move'both Ieftwa'rdly and upwardly over the twin cam rollers 5! whose shaft rests in the bottom of the slots 54 ;and 55 and so cannot move downwardly. In moving upwardly thus, thecam 58,1iitfs5the rods 6t and 6! and thus lifts the carri'ag'es. 45 and '48 which run freely in their guide rails but'fcan'nottm ntherein;- I-I ence the rigid bar consisting of the rod 69'fthe'cam 58, and the rod 5! moves*h'-'e;e'lyu arm downias" required by the cam 58 riding over the rollers 51, but cannot The guide rails til-t ii andremains" always parallel" to itself rue cam 58- isfso proportioned'that in all' no'rm'al 70p era'tion it does not come'in' contact with the central overlying cam roller because of the opening 59 (Fig. 10-) in the cam. The carn5'8 does, however, underrun and lift the twin "rollers 54 and therewith the shaft-65am roller 660m which thecanrwedge 5! rests. Thestructures associated witlr'thecarnfi'l areparallel fun'ction and arrangementto those described in con nection with'the cam 58. Hence lifting rthet cam 5 causes the carriages 44 and 49* to'ris'e as I the rigid bar liag 67, H is thus lifted," this bar remaining always parallel to itself. And this manger the cam 6'! aiso raisesthe roller 'l2'and'therewith the stirrup ES-soth at the'cord 1.! and weight actuatethe sheave '18 to movethe pointer over the scale 81 adistance proportionate to The piston. it? being simultaneously given a displace ment y,'causes th'eiwedge N to move horizontally a distance yLand so to ride'over the roller fil: and raise the'roil'er "l2 and stirrup ll-San additional ainount 'to that already effected'or being' 'efiected by the cam 58, to cause the pointer fidto move additionally over'thescale ill *a' distance propertionateto the distance y. Hence, by proper cal 'r-i bration'of thescale Bl, the pointer-8fl=indicates on the scale at any moment; the instantaneous value of the algebraic sum of a: and y; The arrangement shown in Figs, 9; 10 and 11' is thus a complete and operativepractical embodiment of the system showndiagrammatically in Fig. 1; It isnot believed necessarytto discuss indetail the modifications required to convert this intosimilar embodiments of the systems diagrammed in-Figs: 2; 3,- 4 and'5, as these details 'arethought to be merely matters of mechanical design; Fig ll illustrates;however, the modification of theitop center portion ofzFig' 7 to providemeans for recording graphically continuous combined values as inFigs. 2, -and 26 instead of indicating in-' stantaneous combined valuesas in Figs-=1, 3, 5 and '7.

Fig; 11 bears generally. the same relatiomto Fig. 7 that Fig. 6 does to Fig. 1. The outer end of the piston rod- I5lcarries a cam roller 8%} which runs against a cam 81 which in turn may" conveniently run ina' guide base iidmounted onthe rail-=58 and having ball bearing rollers '39 for the straight inner-edge-of the-cam Elli to run on. The cam 81 is preferably a stiiiiy rigidand hard lamina (if-suitable material, e. g. metal, plastic, woodor the like, which is interchangeably secured, as by bolts 9G; to a vertically ex-: tending biturcate driving member 9,! in which is mounted a cam roller 92; The roller 92 runson an adjustable wedge-cam generally indicated' atreciprocable horizontally ina base 9d which may conveniently be mounted'on the top of the The cant-93 comprises a base bar 55'slid'ablein the base 94 with a pitch bar 96 pivoted thereto' a-t the left-end and on which the-roller -92 runs. The angle A between these bars is adjustable by means of the block 91 movable between the bars by the screw-il8 pass ing through the nut 99 fixed on the bar 95. There is a duplicate structure and arrangement on the left side of the apparatus where a wedge cam generally indicated at l 93,adjustab1e as to its angle B by a screw [98,"acts to drive an inter 7 Fig. 7 are omitted. A vertical rod IT! is mounted on the stirrup I6 instead of the cord and extends upwardly. A tracing point I 80 is mounted on the rod IT! to run vertically across a paper tape I8! driven horizontally at constant speed by any suitable means not shown.

The cams 87 and I8! are formed to the curves of any desired continuous single valued functions f(u) and F(u), respectively. Then if the wedge cam 93 be driven leftwardly at constant speed 25, the cam 87 is lifted at constant speed at where a is tan A. The piston I62 then, and therefore the piston 82, move rightwardly at the speed )(at) and the drive cam I58 leftwardly at this speed, rightwardly whenever flat) is diminishing. The cam I58 then drives the rollers 84, 64 and so the wedge cam I6! upwardly at a speed df(at) where d is tan D. Now if the cam I93 be driven rightwardly simultaneously at the same speed If, the wedge cam 16! while being lifted in the manner just described will further lift the roller I2 and therewith the tracer point I88 at a speed eF(bt), where e is tan E and b is tan B. Hence when cams 93 and I93 are simultaneously driven at the same rate, the tracer point I80 is moved across the tape I8I at the rate dflat) plus eF(bt) and will trace the graph of this sum on the uniformly moving tape.

Thus the apparatus disclosed in Fig. 11 is a complete and operative embodiment of the arrangement diagrammatically illustrated in mg. 6. The bases 88 and 94 on the right and I88 and I94 on the left are shown, for simplicity and convenience of illustration, as mounted on the guide rails of the carriages. In practice it may be preferable to mount these aside from and independently of the rails.

It is worthy of note, in connection with Fig. 11, that if the wedge cam I93 be not driven but left stationary, the apparatus will convert the value 2? into dfiat) thus making it a device for altering the vertical or horizontal scale or both of the graph of the function fit).

Since the character and value of the invention do not depend upon whether a pointer and scale such as 88 and BI or a recording point I80 and tape I8I are used the phrase result member will be used in the appended claims to signify any useful means by which the motion of the stirrup 16 or its equivalent may be either observed or recorded. a

It will be noted that in the arrangements disclosed in Figs. 1, 4, and '7, the shift of the result member 27 or 16 due solely to the cam action of the cam 2|, 32I or 58 is directly proportional to the change in the position of the cam due to change of the variable value :1:. On the other hand, in the arrangements disclosed in Figs. 2, 3, 6 and 11, the shift of the result member 21 or 16 due solely to the cam action of the cam I2I, 22 I, 42I or I58 is not in fixed ratio to the change in the value a: or t since the cams I 2| and 22I are shaped to other than linear functions and the non-linear cams 49 and 8'! are interposed respec tively between the cams 42 and 42I, or between the cams 93 and I58. In each case the motion corresponding to a: or t is converted into the corresponding part of the motion of the result member by means comprising an interposed cam shaped to correspond to some single valued, continuous mathematical function. In Figs. 1, 4, 5 and 7, the function in question is linear, the cam is in effect a straight sided wedge, and the change in position of the result member due to a change in the value a; or t is in constant ratio thereto. In Figs. 2, 3, 6 and 11 the two changes are not in constant ratio to each other, because there is an interposed cam which is formed to correspond to a non-linear function. Nevertheless, there is a one-to-one relation between these changes defined by the cam in question. The change in position of the result member is determined positively by the change in a: or t. The relation disclosed in Figs. 1, 4, 5 and 7 is a special case of the class of relations disclosed in Figs. 2, 3, 6 and 11. There being no familiar word or convenient phrase available for this state of affairs, in the following claims the word relation in such phrases as a cam member movable in relation to a quantity shall be taken to mean that variation of the quantity is reflected in a motion of the cam member such that there is a definite, predetermined functional correspondence between the two, which may be a simple, constant ratio as in Fig. 1 or may be any desired predetermined single valued, continuous function over the range of variation in question. Similarly, in the appended claims, the term function cam shall be taken to mean a cam means whose cam surface is formed, as illustrated in any of Figs. 1, 2, 3, 4, 5, 6, 7 and 11, to correspond to a continuous portion of the graph of any desired, predetermined mathematical function, linear, algebraic, transcendental or whatever.

What is claimed is:

1. In an apparatus for combining plural variable quantities, a first linear cam movable proportionately to one quantity to be combined, an interchangeably mounted function cam representing a second quantity and driven by the first cam, a second linear cam driven by said function cam, a support shiftable by said second cam, means for guiding the support in a predetermined path, a third linear cam movable proportionately to a third quantity to be combined, a second interchangeably mounted function cam representing a fourth quantity and driven by said third linear cam, a fourth linear cam operable by the said second function cam and mounted on the support to be shiftable therewith and to be movable thereon, and a result member operable by the shifting of said last cam.

2. A device according to claim 1 wherein said first and third linear cams comprise adjustable wedges whereby a further factor may be introduced at each of said cams.

3. A device according to claim 1 wherein all of said linear cams comprise adjustable wedges whereby additional factors may be introduced at each of said cams.

4. An apparatus according to claim 1 wherein flexible driving means are provided between the function cams and the linear cams driven thereby to permit multidimensional movement of the said driven linear cams.

WILLIAM F. DEHN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 580,783 Fuller Apr. 13, 1897 1,453,688 Milker May 1, 1923 1,520,514 Snodgrass Dec. 23, 1924 (Other references on following page) Number Number 10 FOREIGN PATENTS Country Date Great Britain Feb. 7, 1918 Great Britain Apr. 28, 1921 Great Britain Feb. 26, 1923 Great Britain June 5, 1928 Germany June 17, 1925 Great Britain Jan. 20, 1939 France Feb. 20,1925 Germany June 6,1936 France Nov. 23, 1931 

